A frequently recurring problem in communications is the need to accurately represent the spectrum a signal in order to perform various signal processing techniques on the signal (e.g., remove noise and interference). Cross terms in a signal make it difficult for prior art time-frequency methods to isolate individual components in the signal.
Prior art time-frequency methods describe the density of a signal's energy as a joint function of time and frequency, and frequently make two assumptions: (1) density is nonnegative and (2) what are the energy marginal conditions. The energy marginal conditions require that the integral of the time-frequency density with respect to frequency (time) for fixed time (frequency) equals the magnitude square of the signal (signal's Fourier transform) at time (frequency).
Mapping from signals to their conventional time-frequency densities (surfaces) is not linear, since the marginal conditions are not linear. That is, the magnitude square of the sum of the two signals (signals' Fourier transforms) is not the sum of the magnitudes of the individual signals (signal's Fourier transforms). Consequently, enforcing the energy marginal conditions for a multi-component signal requires that additional cross-term energy, not present in the time-frequency densities of individual components, must be spread over the time-frequency surface of the composite signal. This makes it difficult, if not impossible to use conventional time-frequency methods to generate a time-frequency representation of the individual components of a multi-component signal.
Many of the problems associated with prior art time-frequency methods may result from distributing a non-linear quantity. The basis for this is that while signals add, their corresponding energies do not. The present invention overcomes the problem associated with the prior art time-frequency methods.
U.S. Pat. No. 6,434,515, entitled “SIGNAL ANALYZER SYSTEM AND METHOD FOR COMPUTING A FAST GABOR SPECTROGRAM,” discloses a method of computing a time-varying spectrum of an input signal using a multi-rate filtering technique. The present invention does not use a multi-rate filtering technique as does U.S. Pat. No. 6,434,515. U.S. Pat. No. 6,434,515 is hereby incorporated by reference into the specification of the present invention.